Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Find the sum of all three-digit numbers each of whose digits is
This activity involves rounding four-digit numbers to the nearest thousand.
Are these statements always true, sometimes true or never true?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Here are two kinds of spirals for you to explore. What do you notice?
An investigation that gives you the opportunity to make and justify
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What happens when you round these three-digit numbers to the nearest 100?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge asks you to imagine a snake coiling on itself.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
This challenge is about finding the difference between numbers which have the same tens digit.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
A collection of games on the NIM theme
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?